Effective Parameters of Hydrogeological Models

193 Pages·2014·3.857 MB·English

by  Gorokhovski, Vikenti

Springer Hydrogeology
Vikenti Gorokhovski
Effective
Parameters of
Hydrogeological
Models
Second Edition
Springer Hydrogeology
For furthervolumes:
http://www.springer.com/series/10174
Vikenti Gorokhovski
Effective Parameters
of Hydrogeological Models
Second Edition
123
Vikenti Gorokhovski
Athens,GA
USA
ISBN 978-3-319-03568-0 ISBN 978-3-319-03569-7 (eBook)
DOI 10.1007/978-3-319-03569-7
SpringerChamHeidelbergNewYorkDordrechtLondon
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(cid:2)SpringerInternationalPublishingSwitzerland2014
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Dedicated to my wife
Inna Gorokhovskaia
and
to the memory of our son
Iaroslav Gorokhovski
(1963–2011)
Preface to Second Edition
Themainchangemadeinthiseditionisanewchapter,Chap.10,locatedbetween
Chaps.9and10ofthepreviousedition.Itpresentsthemethodbasedonsimulation
of advective solute transport through porous media with direct inclusion of
hydrodynamic dispersion. The method reduces solute transport simulation to
solving partial differential equations of the first order for different actual pore
water velocities which makes it very flexible. The ways of evaluating the actual
pore water velocities are suggested also. The method is an alternative to the
classical convective-dispersion model with it fictitious dispersion coefficient and
themeanactualporevelocity,excludinghydraulicdispersion,themainreasonfor
appearance of long tails of the observed breakthrough curves.
The history of this chapter appearance is following. A known hydrogeologist
stated to Dr. Steven Kraemer, my supervisor at that time, that the use of the first
type boundary condition in simulation of solute transport in porous media is
incorrect. He suggested overwriting all related software used by Environmental
ProtectionAgency, U.S.A.,applying the boundaryconditionofthe third type, the
flux condition, the only correct boundary condition, according to him. Before
discussing the issue with his supervisors, Steve asked me to clarify the situation.
The most detail basis for introducing the flux boundary condition which I could
findistheworkofParkerandvanGenuchten(1984).Inmyopinionthebasiswas
unsatisfactory,doubtfulmathematicallyandphysically,whichIreportedtoSteve.
After becoming afreelance hydrogeologist,Igotmorefreetime andtook partin
discussion (Gorokhovski 2013) on Batu (2010) holding that the flux condition is
the only correct one becauseit keeps mass-balance at the inlet.In the response to
mycriticism,(Batuetal.2013)donotrefutemyargumentsbutcontinueinsistthat
thefluxboundaryconditionistheonlycorrectone.Itisobviousthattheuseofthe
mean pore velocity inthe classical model eliminates hydraulic dispersionfrom it.
The empirical dispersion coefficient should, as if, compensate for the hydraulic
dispersion.Howthisfictitiouscoefficientdoesthejobwasneverexplained,andit
does not factually. Long tails of the observed breakthrough curves exists due
mostlyhydraulicdispersion.Theimpossibilityinmostcasestoreproducethemby
simulation breakthrough curves is clear demonstration of this. The issue offitting
the simulation breakthrough curves into the observed long tailed ones was the
main motivation for Parker and van Genuchten (1984) to introduce the flux
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boundary condition. Likely, its application did not resolve the issue (Parker and
van Genuchten 1984; Paseka et al. 2000; Delleur 2006; Dušek et al. 2007;
Appuhamillage et al. 2010).
Other changes include reviews ofsomeworksappeared after publishing of the
first edition of this book or related to Chap. 10. Thus, in distinction from the
previous edition, all examples related to solute transport are concentrated in this
chapter to minimize the necessary changes in the book. Few misprints and inac-
curacies slipped into the previous text were corrected also.
Acknowledgments
IwouldliketoexpressmygratitudetoDr.StevenKraemer,myfriendandoneof
my supervisors, without whose suggestion to clear up the issue with the flux
boundaryconditioninsolutetransportsimulationthiseditionwouldneverhappen.
Asusual,mywifeInnaandoursonVikentiweresupportiveandextremelyhelpful
in my work.
References
AppuhamillageTA,BokilVA,ThomannE,WaymireE,WoodBD(2010)Solutetransportacross
an 20 interface: A Fickian theory for skewness in breakthrough curves. Water Resour Res
46:21doi:10.1029/2009WR008258
Batu V (2010) Estimation of degradation rates by satisfying mass balance at the inlet. Ground
Water48(4):560–568
BatuV,vanGenuchtenMT,ParkerJC(2013)ResponsetothecommentbyGorokhovski(2013)
GroundWater51(1):9–11
DelleurJV(2006)ElementaryGroundwaterFlowandTransportProcesses.In:DelleurvJV(ed)
Chap.3inHandbook:GroundwaterEngineering,2ndedn.CRCPress,BocaRacto,pp.1,320
Dušek J, Dohnal M, Vogel T (2007) Pollutant transport in porous media under steady flow
conditions.http://www.cideas.cz/free/okno/technicke_listy/4tlven/TL07EN3112-6.pdf,Czech
TechnicalUniversityinPrague
GorokhovskiV(2013)Technicalcommentaryon‘‘Estimationofdegradationratesbysatisfying
massbalanceattheinlet’’byVadatBatu,GroundWater51(1):5–7
Parker JC, van Genuchten MT (1984) Flux-averaged and volume-averaged concentrations in
continuumapproachtosolutetransport.20(7):866–872
PasekaAI,IqbalMZ,WaltersJC(2000)Comparisonofnumericalsimulationofsolutetransport
withobservedexperimentaldatainasiltloamsubsoil.EnviroGeo39(9):977–989
Preface to the First Edition
Thisbookconcernstheuncertaintyofthehydrogeologicalmodeling.Inasense,it
isadevelopmentoftheideaspublishedlongago(Gorokhovski1977).Thetopicof
thatbookwasimpossibilityofevaluating theuncertaintyofthesimulation results
inaprovablequantitativeway.Thebookhappenedtobeasuccess:Ihaddifficulty
finding its copies for my friends, some prominent hydrogeologists and geological
engineers started treating me with more respect, and some colleagues stopped
speaking to me for a long time. But no other consequences followed.
I personally was not fully satisfied. The book was mostly a critique based on
common sense and illustrated by simple and transparent examples from hydro-
geology and geological engineering. The examples could be easilyverified, using
justacalculator.Thebookstatedthattheimpossibilitytoevaluatetheuncertainty
of simulation results does not preclude obtaining the results which are best in a
reasonably defined sense, though the uncertainty of those best results remains
unknown. But I had a vague notion on how to assure such results at that time.
Quantitative predictions of responses of geological objects on man made and
naturalimpactswere,are,andwillremainintheforeseeablefutureaconsiderable
elementofengineeringdesignanddecisionmaking.Eveninthattimeandevenin
the Soviet Union, where I resided and worked, it was possible to simulate many
applied hydrogeological processes, though access to the pertinent software and
computers was not easy, at least for me (see Afterword for more details). At
present,duetothefastdevelopmentofcomputersandnumericalmethods,wecan
simulate almost any process based on contemporary concepts and theories. The
gravestobstacleremainsuncertaintyofthesimulationresultscausedbypaucityof
the available data on properties of geological objects, boundary conditions, and
impacts whenthe natural impacts are affectingfactors.So oneofthe main issues,
inmyopinion,ishowtoassurethattheyieldedresultsarethebest,effective,inthe
senseasthebestisdefined.Ihopethatthisbookisaconsiderablesteptoyielding
the effective simulation results.
Theuncertaintyoftheresultsofhydrogeologicalmodelingwasandisdiscussed
intensively.Thus,Beck(1987)writes:‘‘Thedifficultiesofmathematicalmodeling
are not questions of whether the equations can be solved and the cost of solving
themmanytimes;notaretheyessentiallyquestionsofwhetherpriorytheories(on
transport, dispersion, growth, decay, predation, etc.) is potentially capable of
describing the system’s behavior. The important questions are those whether the
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x PrefacetotheFirstEdition
priory theory adequately matches observed behavior and whether the predictions
obtainedfrommodelsare meaningfulanduseful’’.Oreskesetal.(1994) holdthat
geological models ‘‘predictive value is always open to question’’. (See also,
Oreskes2003,2004).Thisisnotsurprising,sinceinhydrogeology‘‘themodeling
assumptions are generally false and known to be false’’ (Morton 1993, Beven
2005). I could continue this list of similar quotations. But let me restrict myself
with one more. As Beven (2004), puts it mildly: ‘‘There is uncertainty about
uncertainty’’.Ithinkheiswrong:theuncertaintyofthehydrogeologicalmodeling
isthefactaboutwhichthereisnouncertainty.Indeed:‘‘It’safundamentaltenetof
philosophy of science that the truth of a model can never be proved; only dis-
proved,’’ (Mesterton-Gibbons 1989).
The above quotations are a tribute to academism really. Experienced hydrog-
eologists are well aware of the uncertainty of most their conclusions. And the
reason is obvious. The models include properties and combinations of the prop-
erties of geological objects. Those must be known continuously, at least, when
differentialorintegralequationsareinvolved.Thatis,theymustbeknownateach
point of the object and at each instant of the simulation period, excluding sets of
isolated points and instants. But geological objects are inaccessible to direct
observations and measurements and the data on them are sparse. The geological
modelsareatooltointerpolateandextrapolatethesparsedataateverypointofthe
geological object which they represent in simulations and at very instant of the
periods of the simulations. The tool is limited. The geological interpolation and
extrapolationarebasedontheprinciplethatgeologicalsettingsofthesameorigin,
composition,andgeologicalhistoryhavethesameproperties.Thisprincipleleads
toso-calledpiecewisehomogeneousgeologicalmodels.Sometimes,theproperties
are subjected to spatial trends whose mathematical descriptions are arbitrary in
essence(Chap. 3).Sohowcanweevaluateinaquantitativewaythereliabilityof
thegeologicalmodelswithrespecttoaproblemathand?Itsufficesjustacommon
sense to conclude that it is impossible except, maybe, in some rare cases.
Sincetheissueis notsimulations,solving thecorresponding equations,butthe
uncertaintyoftheyieldedresults,thequestionarises,whattodo?U.S.EPA(1987)
gives the answer related to environmental predictions, including hydrogeological
ones: ‘‘It should be recognized that the data base will always be inadequate, and
eventually there will be a finite sum that is dictated by time, common sense, and
budgetary constraints. One simply has to do the best one can with what is avail-
able’’. Unfortunately, (U.S. EPA, 1987) does not explain what is and how to do
‘‘the best’’.
The situation seems to be clear enough: it is impossible to evaluate the
uncertainty of simulation results of the hydrogeological models in a provable
quantitativeway.But,contrarytoitsown statementcited above U.S. EPA(1989)
holdsthat‘‘Sensitivityanduncertaintyanalysisofenvironmentalmodelsandtheir
predictions should be performed to provide decision -makers an understanding of
thelevelofconfidenceinmodelresultsandtoidentifykeyareasforfuturestudy’’.
Itclaimsalsothat‘‘Anumberofmethodshavebeendevelopedinrecentyearsfor
quantifying and interpreting the sensitivity and uncertainty of models’’. NCR
PrefacetotheFirstEdition xi
(1990) states ‘‘Over the past decade, the development of stochastic modeling
techniques has been useful in quantitatively establishing the extent to which
uncertainty in model input translates to uncertainty in model prediction’’. Binley
and Beven (1992), Beven and Freer (2001) and Beven (2005), suggest a general
likelihood framework for uncertainty analysis, recognizing that it includes some
subjectiveelementsand,therefore,inmyopinion,maynotbeprovable.Hilletal.
2000,suggestthealgorithmandprogram,permittingevaluatingtheuncertaintyof
simulation results. Cooley, 2004, suggests a theory for making predictions and
estimatingtheiruncertainty.Andsoon(FeyenandCaers2006;Hassanetal.2008;
Rojas et al. 2008,2010;Chand Mathur 2010; Mathonet al. 2010; Ni el at.2010;
Singh et al. 2010a, b; Zhang et al. 2010; Doherty and Christensen 2011, and
others).
Forexample,DohertyandChristensen(2011)holdintheabstracttotheirpaper
thatit‘‘describesamethodologyforpairedmodelusagethroughwhichpredictive
bias of a simplified model can be detected and corrected, and postcalibration
predictiveuncertaintycanbequantified’’.However,theywriteclosertotheendof
their paper: ‘‘In designing and implementing the methodology discussed herein,
wehaveassumedthattheprocessesandconstructiondetailsofthecomplexmodel
approximate those of reality. It is obvious that this will not always be the case.
Indeed,eventhemostcomplexmodelisquitesimplecomparedtorealityitself.In
spiteofthis,amodelercanonlydohisorherbest’’.Somethinglikethishasbeen
already quoted (EPA, 1987). But let us continue. Several lines below their pre-
vious statement Doherty and Christensen (2011) write: ‘‘Nevertheless, the less
than perfect nature of a complex model, and its consequential failure to represent
all nuances of system behavior, may indeed result in some degree of underesti-
mation of predictive uncertainty. This, unfortunately, is unavoidable’’.
I pay more attention to the work of Doherty and Christensen (2011) not only
because it is one of the most recent ones on the uncertainty of hydrogeological
simulation, but because it is typical. Many, if not most, of such publications
proclaim in the very beginning that a method of quantifying of the simulation
uncertaintyisbeingsuggested.However,somewhereclosertotheend,theauthors
explain that they can estimate the uncertainty to some degree. The authors, being
excellentmathematicians,understandthattheirsimulationsarebasedonanumber
ofexplicitandimplicitassumption,hypotheses,andsimplificationsmostofwhich
cannot be validated or are knowingly false. So their estimates of the uncertainty
arenotprovable.Thisisfromwhereallthese‘‘tosomedegree’’appear.ThePolish
poetandaphoristJerzyLectoldaboutsuchkindofsituations:‘‘Impolitelytospeak
‘it seems’ when everything is already clear’’.
Doherty and Christensen (2011) attracted my attention also because their
methodology of the paired modelusage,at first glance, seems tobesimilarto the
two-level modeling described in this book and presented previously, in various
contextsrelatedtoitsdifferentpossibleuse(Gorokhovski1986,1991,1996,2012;
Gorokhovski and Konivetski 1994; Gorokhovski and Nute 1995, 1996). While
seemingly alike, the paired model usage and the two-level modeling differ with
respect to their mathematics and goals. The goal, as well as mathematics, of the